It takes Kim 26 minutes to type and spell check 14 pages of a manuscript. Find how long it takes
her to type and spell check 77 pages.

Answer:

firstly,need to know domain and range

Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

Using the normal distribution, it is found that:

a) The interval that will contain most of the GPA's is (1.79, 4.43).

b) The z-score associated with this grade is of -2.82 < -2, thus, it is unlikely that this student studied 3 hours per day.

-----------------

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

-----------------

-----------------

Item a:

\(3.11 - 2(0.66) = 1.79\)

\(3.11 + 2(0.66) = 4.43\)

The interval that will contain most of the GPA's is (1.79, 4.43).

-----------------

Item b:

We have to find the z-score when \(X = 1.25\), thus:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{1.25 - 3.11}{0.66}\)

\(Z = -2.82\)

The z-score associated with this grade is of -2.82 < -2, thus, it is unlikely that this student studied 3 hours per day.

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Answer:

Step-by-step explanation:

it is the diameter AB.

An equation of the line that goes through the point (-1, -3) and (3, 5) is y = 2x - 1.

An equation of the line in slope-intercept form that is perpendicular to the equation for obstacle 1 is y = -x/2 + 3.

In Mathematics, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁) or \(y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\)

Where:

At data point (-1, -3), a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

\(y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\\\\y - (-3) = \frac{(5- (-3))}{(3-(-1))}(x -(-1))\\\\y +3 = \frac{(5+3)}{(3+1)}(x +1)\)

y + 3 = 2(x + 1)

y = 2x + 2 - 3

y = 2x - 1

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

2 × m₂ = -1

m₂ = -1/2.

At point (-4, 5), an equation of the line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -1/2(x + 4)

y = -x/2 - 2 + 5

y = -x/2 + 3

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Answer:

The direction of mathematics teacher is study about the mathematics teacher is study about it is by step instructions

Answer:

The matrix that represents the system of equations is:

\(\left[\begin{array}{ccc}0&1&10\\4&-5&3\end{array}\right]\)

Step-by-step explanation:

We will use the first column for x, the second to y and the last for the independent term.

We have:

\(y=10\rightarrow0x+1y=10\\\\4x-5y=3\)

Then, we can write the matrix to represent the system of equations as:

\(\left[\begin{array}{ccc}0&1&10\\4&-5&3\end{array}\right]\)

Answer:

25=r+5

he worked 20

Step-by-step explanation:

The measures of the angles to the nearest degree are:

a) A ≈ 36 degrees

b) B ≈ 23 degrees

c) C ≈ 2 degrees

To find the measure of the angle to the nearest degree given trigonometric ratios, we can use inverse trigonometric functions.

Here are the steps to determine the angles:

a) sin A = 0.6018

Taking the inverse sine (arcsin) of both sides:

A = arcsin(0.6018)

Using a calculator, we find A ≈ 36 degrees (rounded to the nearest degree).

b) cos B = 0.9205

Taking the inverse cosine (arccos) of both sides:

B = arccos(0.9205)

Using a calculator, we find B ≈ 23 degrees (rounded to the nearest degree).

c) tan C = 0.0349

Taking the inverse tangent (arctan) of both sides:

C = arctan(0.0349)

Using a calculator, we find C ≈ 2 degrees (rounded to the nearest degree).

Therefore, the measures of the angles to the nearest degree are:

a) A ≈ 36 degrees

b) B ≈ 23 degrees

c) C ≈ 2 degrees.

Note: Trigonometric functions have periodicity, meaning there may be multiple angles with the same trigonometric ratio.

To determine the principal angle within a specific range, we use the inverse trigonometric functions.

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The equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

To find the equation of a line that passes through the point (-1, 3) with a slope of 1, we can use the point-slope form of a linear equation.

The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

where (x1, y1) represents the coordinates of a point on the line, and m represents the slope of the line.

Using the given point (-1, 3) and slope 1, we substitute these values into the point-slope form equation:

y - 3 = 1(x - (-1))

Simplifying:

y - 3 = x + 1

Now, we can rewrite the equation in the standard form:

y = x + 4

Therefore, the equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

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Answer:

a four-sided plane rectilinear figure with opposite sides parallel.

Step-by-step explanation:

Answer:

Parallelograms are a type of quadrilateral, which is a polygon with four sides. A parallelogram is a specific type of quadrilateral that has two pairs of parallel sides. This means that the opposite sides of a parallelogram are parallel and equal in length.

In addition to having parallel sides, parallelograms also have some other notable properties:

Opposite angles are congruent: The opposite angles of a parallelogram are equal in measure. This means that if you label the angles A, B, C, and D, then angle A is congruent to angle C, and angle B is congruent to angle D.

Step-by-step explanation:

Answer:

t = 6.8 years

Step-by-step explanation:

The formula for compound interest is

\(A(t)=P(1+r/n)^n^t\), where P is the principal/amount invested, r is the interest rate, n is the number of compound periods per year (4 for quarterly), and t in the time in years.

We know that A = $5900, P = $4000, and r = 0.0575 (we must convert the percentage to a decimal).  We must solve for t and round to the nearest tenth:

\(5900=4000(1+0.0575/4)^(^4^t^)\\\\59/40=(1623/1600)^4^t\\\\log(59/40)=log(1623/1600^4^t)\\\\log(59/40)=4t*log(1623/1600)\\\\log(59/40)/log(1623/1600)=4t\\\\1/4(log(59/40)/log(1623/1600))=t\\\\6.80773607=t\\\\6.8=t\)

Answer: 4.40

Step-by-step explanation: 10 divided by 4 is 2.5 and 2.5 times 4.40=11

so 4.40x2.5=11

Let the unknown number be x.

Negative 48 decreased by a number: -48 - x

Is the same as the sum of 4 times a number and 7:

-48 - x = 4x + 7

Let's find the number:

-48x - x = 4x + 7

-48x = 4x + 7

Subtract 4x from both sides:

-48x - 4x = 4x - 4x + 7

-52x = 7

Step-by-step explanation:

4(y+8)=9

for this sum first we need to multiply 4to y and 4 to 8

4y+32=9

then u need to -9 from both sides

4y=23

y=23/4

u will get the answer

The translations that map to the four tiles are 1 to 2: (x,y) → (x + 2, y), 1 to 4: (x,y) → (x, y + 2), 1 to 6: (x,y) → (x + 4, y + 2) and 1 to 8: (x,y) → (x + 2, y + 4)

From the question, we have the following parameters that can be used in our computation:

The graph

From 1 to 2, we can see that the figure is shifted to the right by 2 units

This is represented as

1 to 2: (x,y) → (x + 2, y)

From 1 to 4, we can see that the figure is shifted up by 2 units

This is represented as

1 to 4: (x,y) → (x, y + 2)

From 1 to 6, we can see that the figure is shifted up by 2 units and shifted right by 4

This is represented as

1 to 6: (x,y) → (x + 4, y + 2)

From 1 to 8, we can see that the figure is shifted up by 4 units and shifted right by 2

This is represented as

1 to 8: (x,y) → (x + 2, y + 4)

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Answer:

D.

Step-by-step explanation:

it should be the sales tax because you pay a little bit more.

Answer:

hmmm

Step-by-step explanation:

Answer:

==============

Since both points have same x-coordinate, the distance between them is the difference of y-coordinates:

Correct choice is D

Answer:

32 units

Step-by-step explanation:

\(\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}\)

Define the two given points:

Substitute the two points into the distance formula and solve for d:

\(\implies d=\sqrt{(-7-(-7))^2+(8-(-24))^2}\)

\(\implies d=\sqrt{(-7+7)^2+(8+24)^2}\)

\(\implies d=\sqrt{(0)^2+(32)^2}\)

\(\implies d=\sqrt{32^2}\)

\(\implies d=32\)

Note: As the two given points have the same x-coordinate, the line segment (between the points) is a vertical line. Therefore, to find the distance between the two given points, simply calculate the difference between the y-coordinates:  

\(\implies 8 - (-24) = 8+23=32\)

Answer:

It will take Walter 112.5 minutes to complete the project by himself

Step-by-step explanation:

The together rate is the sum of each separate rate.

In this problem:

Together rate: 1/45

George's rate: 1/75

Walter's rate: 1/x

How long will it take Walter to complete the project by himself?

This is x. So

\(\frac{1}{75} + \frac{1}{x} = \frac{1}{45}\)

\(\frac{x + 75}{75x} = \frac{1}{45}\)

\(75x = 45(x + 75)\)

\(75x = 45x + 45*75\)

\(30x = 45*75\)

\(x = \frac{45*75}{30}\)

\(x = 112.5\)

It will take Walter 112.5 minutes to complete the project by himself

Answer:

1 = 130° , 2 =50° , 3 = 85°, 4=45°

Step-by-step explanation:

1 =45 + 85 = 130 { sum of opposite interior angle equals exterior angle}

2 = 180 - 1 { angles on a straight line equals 180}

= 180 -130 = 50°

4 = 180 - 135 = 45° { angles on a straight line equals 180}

3 = 135 -2 { sum of opposite interior angles equals exterior angle; 3 + 2 = 135}

3 = 135-50 = 85°

Note : sum of opposite interior angles equals external exterior angle, let's prove it:

If we look at the triangle at the bottom left, we have :

85, 45 and r { let's denote r as the missing angle}

So 85 + 45 + r = 180° { sum of angles of a triangle}

By simple arithmetic

r = 180 - ( 85+45) = 180 - 130 = 50°

but r + 4 = 180° { sum of angles in a straight line equals 180°}

4 = 180 - 50 = 130°

So you see 4 is the exterior angle of the triangle opposite to 85° and 45° interior angles}

Answer: The answer is 8 1/3

I hope this helps

Step-by-step explanation:

Answer:

the answer for your question is 8 1/3

Answer:

D?

Step-by-step explanation:

\( \sf \: Volume \: is \: calculated \: in \: cubic \: units \: ( {units}^{3} ) \: \\ \sf \: because \: we \: use \: volume \: to \\ \sf \: measure \: the \: space \: enclosed \: by \: \: 3 \: dimensional \: (3-D) \\ \sf \: figures \: like \: cuboid, \: cube, \: cylinder \: etc.\)

The line is:

y = 400*x + 2000

And the statements are:

The original purchase price of the computer is given by the y-intercept, which is $2,000

The change in the price of the computer is the slope, which is 400.

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

slope = (y2 - y1)/(x2 - x1)

Using the graph we can identify two points like:

(1, 1600) and (5, 0)

Then the slope is:

a = (0 - 1,600)/(5 - 1) = 400

And the y-intercept is 2,000, as we can see on the graph.

Then the line is:

y = 400*x + 2,000

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The correct comparison of the population and sampling distribution is A. Means are the same but the standard deviation of sampling distribution is smaller

X X^2

95 9025

96 9216

98 9604

Sum = 289 27845

n 3

The sample mean 96.33333333 SUM/n

Population mean 96.33333333 SUM/n

Sample standard dev \(1.527525232 \sqrt{((1/(n-1))(SUM(X^2)-(1/n)SUM(X)^2)}\)

Population standard dev \(1.247219129 \sqrt{((1/n)(SUM(X^2)-(1/n)SUM(X)^2)}\)

Population Mean(μ) = 96.33

Population standard deviation (σ) = 1.25

Option A) 95,96,98 and X bar = 96.33

Sampling distribution :

mean (μx = μ) = 96.33

standard deviation(σx = σ/SQRT(n)) = 1.25/SQRT(3) = 0.72

Option A) Means are the same but the standard deviation of the sampling distribution is smaller

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Answer:

C and D.

Step-by-step explanation:

C is ( 1 , 1 ) and D is ( -2.5 , -1.5 )

Tamara should expect the sum of the two cubes to be equal to 7 around 30 times when rolling the two number cubes 180 times.

To determine how many times Tamara should expect the sum of the two number cubes to be equal to a certain value, we need to analyze the chart and calculate the probabilities.

Let's examine the chart and count the number of times each sum occurs:

Sum: 2, Occurrences: 1

Sum: 3, Occurrences: 2

Sum: 4, Occurrences: 3

Sum: 5, Occurrences: 4

Sum: 6, Occurrences: 5

Sum: 7, Occurrences: 6

Sum: 8, Occurrences: 5

Sum: 9, Occurrences: 4

Sum: 10, Occurrences: 3

Sum: 11, Occurrences: 2

Sum: 12, Occurrences: 1

Now, let's calculate the probabilities of each sum occurring.

Since there are 36 possible combinations when rolling two number cubes, the probability of each sum is the number of occurrences divided by 36:

Probability of sum 2 = 1/36

Probability of sum 3 = 2/36

Probability of sum 4 = 3/36

Probability of sum 5 = 4/36

Probability of sum 6 = 5/36

Probability of sum 7 = 6/36

Probability of sum 8 = 5/36

Probability of sum 9 = 4/36

Probability of sum 10 = 3/36

Probability of sum 11 = 2/36

Probability of sum 12 = 1/36

To find out how many times Tamara should expect a certain sum when rolling the two number cubes 180 times, we can multiply the probability of that sum by 180.

For example, to find the expected number of times the sum is 7:

Expected occurrences of sum 7 = (6/36) \(\times\) 180 = 30

Similarly, we can calculate the expected occurrences for all other sums.

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Answer:

384cm2

Step-by-step explanation:

surface area

12×12=144

10×12/2=60

60×4=240

240+144=384cm2

Answer:

Step-by-step explanation:

The volume of this pyramid in cubic inches is 16.

Given that,

The base and height is 8 and 6.

Based on the above information, the calculation is as follows:

The volume is

= 16